To interpet the results of all the surveys for extra solar planets, it is important to understand the concept of completeness. The Kepler team typically requires at least 3 transits of a single planet before it is considered a candidate. For an Earth-like planet orbiting a Sun-like star this means that Kepler must observe that star for 4 years before it can be sure that there are no planets orbiting the star with a 1 year period. For smaller planets it can take even longer since they are harder to detect. Since it takes time to analyze and publish results we don't yet have statistically conclusive results for planets all the way out to 1 year orbits. Astronomers say that the survey is incomplete.
With that caveat, we can use the stars for which Kepler is complete to draw some broad conclusions about planet sizes and how common they are around stars. The most common types of planets are super-Earths and small-Neptunes. At least half of all stars has at least one planet in this size range. Earth-size planets are less common in the close-in orbits for which Kepler is complete for them, but it still appears that at least one quarter of all stars has an Earth-sized planet orbiting it. Note that this does not mean that these planets are habitable — the Earth-sized planets we are including here are all too close to their stars to harbor liquid water. The large Neptunes and giant planets are less common but including all sizes of planets found by Kepler there appears to be on average one planet per star in the still-incomplete Kepler catalog.
A surprise of extra solar planet detections has been the eccentricities of their orbits. In our own Solar system all the large planets have roughly circular orbits with only small values of eccentricity. This does not seem to be typical of planets in general. The planets found by radial velocities and transits have a range of eccentricities, with some very high (20-40%). The dynamics of these systems are fascinating. Explaining how such highly elliptical orbits develop and can be stable over long periods of time is a current challenge in astronomy.
Related to problem of survey completeness is the concept of selection effects. Whenever an observational survey chooses targets it does so according to some criteria. These criteria affect the results and can limit the applicability of the conclusions. This doesn’t mean that the results are wrong, rather that the selection criteria must be considered when analyzing the results. As an example of this, consider the case of "hot Jupiters." This population of planets was revealed by the radial velocity surveys and posed a significant challenge to our understanding of planet formation and evolution. These giant planets, with masses equal to that of Jupiter or larger, were detected on very tight orbits — as short as 3 days — where their temperatures would be 1500 Kelvin or higher. In fact, early on there was a spike in the number of planets occurring right at 3 days. According to the prevailing theory of planet formation, these planets could not form there and so it is believed that they instead migrate there after forming much further out. These radial velocity surveys hinted that hot Jupiters might be common.
To place hot Jupiters in context, first recall how the radial velocity technique works: it detects the reflex motion of the star caused by the gravitational influence of the planet. As such, it is most sensitive to large planets on short period orbits — exactly what was found in the hot Jupiters. Kepler, with its much larger sample size and its much different detection technique, has not found hot Jupiters in large numbers. This doesn’t mean that hot Jupiters are not real. They are and they continue to present a problem for theorists analyzing how planets form. But it does illustrate the challenge and the caution needed when considering the results of exoplanet surveys.
The radial velocity method has yielded the closest known exoplanet. The discovery of a small planet orbiting very close to Alpha Centauri B was announced in late 2012. The Alpha Centauri system is just 4.4 light years away and contains the closest two Sun-like stars. The planet Alpha Centauri Bb has a minimum mass of just 1.13 Earth-masses and orbits at a distance of only 0.05 A.U. with a period of 3.2 days. Like the Kepler circumbinary systems, the fact that this planet exists in a binary star system indicates that planets may be very common.
Another important result from the radial velocity surveys, which give a minimum planet mass, is that the more massive the star the more massive its planets are likely to be. This means that planets like Jupiter become more and more likely as we look at larger and larger stars. An A star like Sirius is twice as likely to have a Jupiter as a G star like our Sun. But another puzzle has emerged in that objects much more massive that Jupiter, from say 10 to 100 Jupiter masses, are not very common around stars of any size. These are what astronomers call brown dwarfs and the lack of such objects gravitationally bound to stars has been termed the "brown dwarf desert." Brown dwarfs are very common on their own, so apparently there is some mechanism that stops planets from growing bigger than 10 times Jupiter& rsqso;s mass.
Gravitational microlensing has contributed to our knowledge of planets as well. The other techniques we have discussed all tend to observe stars relatively close to our Sun. Microlensing by contrast finds planets much further away. Even though only a comparatively small number of planets have been found this way, the larger volume of the Milky Way that is being probed gives these surveys a broad applicability. One exciting result from gravitational microlensing indicates that planets are so common that on average every star in the Milky Way has at least one planet. Note that this is consistent with the hints from the still-incomplete Kepler survey.
The handful of planets detected by direct imaging have themselves raised some interesting challenges for the theory of planet formation. The main theory of planet formation is called core accretion, and it says that planets first form a solid core of about the size of Earth, and then through gravity it attracts a gas envelope or atmosphere. This theory, originally due to Safronov, explains how our own Solar System formed and can account for many of the planets discovered to date. This includes β Pictoris b which was discovered by direct imaging. The planets imaged orbiting HR 8799, however, are too massive and too far from their star to have formed by core accretion. This is because the disk around the star when the planets formed should have been too thin at such wide separations to form a core. A competing theory called gravitational instability may instead explain how these planets formed. In this theory, planets collapse very quickly from the disk without forming a core. Understanding how these different theories explain the diversity of exoplanets is currently one of the hottest topics in astrophysics.